R. B. Karabalin

Piezoelectric nanoelectromechanical resonators based on aluminum nitride thin films

We demonstrate piezoelectrically actuated, electrically tunable nanomechanical resonators based on multilayers containing a 100-nm-thin aluminum nitride (AlN) layer. Efficient piezoelectric actuation of very high frequency fundamental flexural modes up to ~80 MHz is demonstrated at room temperature. Thermomechanical fluctuations of AlN cantilevers measured by optical interferometry enable calibration of the transduction responsivity and displacement sensitivities of the resonators. Measurements and analyses show that the 100 nm AlN layer employed has an excellent piezoelectric coefficient, d_(31)=2.4 pm/V. Doubly clamped AlN beams exhibit significant frequency tuning behavior with applied dc voltage.

Nonlinear dynamics and chaos in two coupled nanomechanical resonators

Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and nonlinear properties. For large vibration amplitudes, the system develops spontaneous oscillations of amplitude modulation that also show period-doubling transitions and chaos. The complex nonlinear dynamics are quantitatively predicted by a simple theoretical model.

Phase synchronization of two anharmonic nanomechanical oscillators.

We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchronized state we demonstrate a significant reduction in the phase noise of the oscillators, which is key for sensor and clock applications. Our work establishes that oscillator networks constructed from nanomechanical resonators form an ideal laboratory to study synchronization--given their high-quality factors, small footprint, and ease of cointegration with modern electronic signal processing technologies.

Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators

In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonators anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nanoelectromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillators phase noise, as predicted by our model.

A Nanoscale Parametric Feedback Oscillator

We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices and opens the possibility of new classes of oscillators employing innovative frequency-determining elements, such as nanoelectromechanical systems (NEMS), facilitating integration with circuitry and system-size reduction. We show that the PFO topology can also improve nanoscale oscillator performance by circumventing detrimental effects that are otherwise imposed by the strong device nonlinearity in this size regime.

Parametric Nanomechanical Amplification at Very High Frequency

Parametric resonance and amplification are important in both fundamental physics and technological applications. Here we report very high frequency (VHF) parametric resonators and mechanical-domain amplifiers based on nanoelectromechanical systems (NEMS). Compound mechanical nanostructures patterned by multilayer, top-down nanofabrication are read out by a novel scheme that parametrically modulates longitudinal stress in doubly clamped beam NEMS resonators. Parametric pumping and signal amplification are demonstrated for VHF resonators up to approximately 130 MHz and provide useful enhancement of both resonance signal amplitude and quality factor. We find that Joule heating and reduced thermal conductance in these nanostructures ultimately impose an upper limit to device performance. We develop a theoretical model to account for both the parametric response and nonequilibrium thermal transport in these composite nanostructures. The results closely conform to our experimental observations, elucidate the frequency and threshold-voltage scaling in parametric VHF NEMS resonators and sensors, and establish the ultimate sensitivity limits of this approach.

Nonlinearity in nanomechanical cantilevers

Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro- and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation.

Stress-Induced Variations in the Stiffness of Micro- and Nanocantilever Beams

The effect of surface stress on the stiffness of cantilever beams remains an outstanding problem in the physical sciences. While numerous experimental studies report significant stiffness change due to surface stress, theoretical predictions are unable to rigorously and quantitatively reconcile these observations. In this Letter, we present the first controlled measurements of stress-induced change in cantilever stiffness with commensurate theoretical quantification. Simultaneous measurements are also performed on equivalent clamped-clamped beams. All experimental results are quantitatively and accurately predicted using elasticity theory. We also present conclusive experimental evidence for invalidity of the long-standing and unphysical axial force model, which has been widely applied to interpret measurements using cantilever beams. Our findings will be of value in the development of micro- and nanoscale resonant mechanical sensors.

Nonlinear Mode-Coupling in Nanomechanical Systems

Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced nanomechanical devices; it has important implications for applications ranging from quantitative sensing to fundamental research. However, achieving accurate experimental characterization of nonlinearities in nanomechanical systems (NEMS) is problematic. Currently employed detection and actuation schemes themselves tend to be highly nonlinear, and this unrelated nonlinear response has been inadvertently convolved into many previous measurements. In this Letter we describe an experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities. By comparing predictions from Euler-Bernoulli theory for the intra- and intermodal nonlinearities of a doubly clamped beam, we assess the validity of our approach and find excellent agreement.

50 nm thick AlN film-based piezoelectric cantilevers for gravimetric detection

Due to low power operation, intrinsic integrability and compatibility with CMOS processing, aluminum nitride (AlN) piezoelectric (PZE) microcantilevers are a very attractive paradigm for resonant gas sensing. In this paper, we theoretically investigate their ultimate limit of detection and enunciate design rules for performance optimization. The reduction of the AlN layer thickness is found to be critical. We further report the successful development and implementation in cantilever structures with a 50 nm thick active PZE AlN layer. Material characterizations demonstrate that the PZE e_(31) coefficient can remain as high as 0.8 C m^(−2). Electrically transduced frequency responses of the fabricated devices are in good agreement with analytical predictions. Finally, we demonstrate the excellent frequency stability with a 10^(−8) minimum Allan deviation. This exceptionally low noise operation allows us to expect a limit of detection as low as 53 zg µm^(−2) and demonstrate the strong potential of AlN PZE microcantilevers for high resolution gas detection.